WorldCat Identities

Stillwell, John

Overview
Works: 50 works in 404 publications in 4 languages and 11,344 library holdings
Genres: History  Textbooks  Sources 
Roles: Author, Translator, htt, Editor, tra
Publication Timeline
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Most widely held works by John Stillwell
Mathematics and its history by John Stillwell( Book )

76 editions published between 1989 and 2011 in 4 languages and held by 2,258 WorldCat member libraries worldwide

Recoge los cambios en esta ciencia desde el teorema de Pitágoras hasta la computación, incluyendo breves biografías de matemáticos eminentes y ejercicios
The four pillars of geometry by John Stillwell( Book )

24 editions published between 2005 and 2010 in English and held by 1,104 WorldCat member libraries worldwide

"The Four Pillars of Geometry approaches geometry in four different ways, devoting two chapters to each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line." "All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers."--Jacket
Classical topology and combinatorial group theory by John Stillwell( Book )

34 editions published between 1980 and 2010 in English and German and held by 1,025 WorldCat member libraries worldwide

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does not understand the simplest topological facts, such as the reason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical develop­ ment where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recrea. ions like the seven bridges; rather, it resulted from the visualization of problems from other parts of mathematics­ complex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject
Elements of algebra : geometry, numbers, equations by John Stillwell( Book )

28 editions published between 1994 and 2011 in English and Italian and held by 873 WorldCat member libraries worldwide

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems
Naive lie theory by John Stillwell( )

26 editions published between 2008 and 2012 in English and held by 788 WorldCat member libraries worldwide

Until recently, lie theory has been reserved for practictioners, with no lie theory for mathematical beginners. This book aims to fill that gap and it covers all the basics at a level appropriate for junior/senior level undergraduates
Roads to infinity : the mathematics of truth and proof by John Stillwell( Book )

16 editions published in 2010 in English and held by 757 WorldCat member libraries worldwide

Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. From publisher description
Geometry of surfaces by John Stillwell( Book )

11 editions published in 1992 in English and held by 712 WorldCat member libraries worldwide

This text intends to provide the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. The geometry of surfaces is an ideal starting point for students learning geometry for the following reasons; first, the extensions offer the simplest possible introduction to fundamentals of modern geometry: curvature, group actions and covering spaces. Second, the prerequisites are modest and standard and include only a little linear algebra, calculus, basic group theory and basic topology. Third and most important, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. They realize all the topological types of compact two-dimensional manifolds, and historically, they are the source of the main concepts of complex analysis, differential geometry, topology, and combinatorial group theory, as well as such hot topics as fractal geometry and string theory. The formal coverage is extended by exercises and informal discussions throughout the text
Elements of mathematics : from Euclid to Gödel by John Stillwell( Book )

20 editions published between 2016 and 2018 in English and held by 579 WorldCat member libraries worldwide

"Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits."--Dust jacket
Yearning for the impossible : the surprising truths of mathematics by John Stillwell( Book )

12 editions published between 2006 and 2008 in English and held by 523 WorldCat member libraries worldwide

"This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. By imbedding mathematics into a broader cultural context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape."--Page ublisher description
Elements of number theory by John Stillwell( Book )

16 editions published between 2002 and 2011 in English and Undetermined and held by 434 WorldCat member libraries worldwide

"This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals." "The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study."--Jacket
Sources of hyperbolic geometry by John Stillwell( Book )

12 editions published between 1996 and 1998 in English and held by 399 WorldCat member libraries worldwide

Reverse mathematics : proofs from the inside out by John Stillwell( Book )

15 editions published between 2018 and 2019 in English and held by 396 WorldCat member libraries worldwide

"This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics."--
Ethnicity and integration by John C. H Stillwell( )

8 editions published in 2010 in English and held by 372 WorldCat member libraries worldwide

The ethnic composition of Britain's population is changing rapidly as the 21st century progresses. Some commentators predict a catastrophic future of increasing ethnic segregation and community breakdown, whereas others say that the benefits of ethnic pluralism and cultural diversity will lead to a more integrated society. This book addresses many of the key issues and debates associated with ethnicity and integration in Britain. It provides the reader with an enhanced understanding of ethnic population change and residential concentration, ethnic household dynamics, internal and international migration, the relationship between ethnicity and health, crime, identity and language, as well as ethnic population projections. Collectively, the findings presented here constitute an evidence base for policymakers and practitioners to draw upon when formulating solutions to the range of problems at local, regional and national level that are associated with an increasingly multi-ethnic society
The real numbers : an introduction to set theory and analysis by John Stillwell( )

13 editions published between 2013 and 2017 in English and held by 365 WorldCat member libraries worldwide

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory"uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis"the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions
Mathematical evolutions( Book )

5 editions published in 2002 in English and held by 255 WorldCat member libraries worldwide

Wahrheit, Beweis, Unendlichkeit : eine mathematische Reise zu den vielseitigen Auswirkungen der Unendlichkeit by John Stillwell( )

6 editions published between 2013 and 2014 in German and held by 126 WorldCat member libraries worldwide

In dem Buch erkundet der preisgekrönte Autor John Stillwell die Konsequenzen, die sich ergeben, wenn man die Unendlichkeit akzeptiert, und diese Konsequenzen sind vielseitig und überraschend. Der Leser benötigt nur wenig über die Schulmathematik hinausgehendes Hintergrundwissen; es reicht die Bereitschaft, sich mit ungewohnten Ideen auseinanderzusetzen. Stillwell führt den Leser sanft in die technischen Details von Mengenlehre und Logik ein, indem jedes Kapitel einem einzigen Gedankengang folgt, der mit einer natürlichen mathematischen Frage beginnt und dann anhand einer Abfolge von historischen Antworten nachvollzogen wird. Auf diese Weise zeigt der Autor, wie jede Antwort ihrerseits zu neuen Fragen führt, aus denen wiederum neue Begriffe und Sätze entstehen. Jedes Kapitel endet mit einem Abschnitt "Historischer Hintergrund", der das Thema in den größeren Zusammenhang der Mathematik und ihrer Geschichte einordnet
Numbers and geometry by John Stillwell( Book )

9 editions published between 1997 and 1998 in English and held by 91 WorldCat member libraries worldwide

"Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis, and geometry - meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions."--Page 4 de la couverture
Papers on group theory and topology by Max Dehn( )

3 editions published in 1987 in English and held by 56 WorldCat member libraries worldwide

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem)
Trees by Jean-Pierre Serre( Book )

7 editions published between 1980 and 2003 in English and Undetermined and held by 48 WorldCat member libraries worldwide

The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by J-P. Serre, and written with the collaboration of H. Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the Bruhat-Tits tree of SL(2) over a local field
Plane algebraic curves by Egbert Brieskorn( )

8 editions published between 1986 and 2015 in English and Undetermined and held by 32 WorldCat member libraries worldwide

I. History of algebraic curves -- 1. Origin and generation of curves -- 2. Synthetic and analytic geometry -- 3. The development of projective geometry -- II. Investigation of curves by elementary algebraic methods -- 4. Polynomials -- 5. Definition and elementary properties of plane algebraic curves -- 6. The intersection of plane curves -- 7. Some simple types of curves -- III. Investigation of curves by resolution of singularities -- 8. Local investigations -- 9. Global investigations -- Bibliography -- Index
 
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The four pillars of geometry
Covers
The four pillars of geometryClassical topology and combinatorial group theoryElements of algebra : geometry, numbers, equationsNaive lie theoryRoads to infinity : the mathematics of truth and proofGeometry of surfacesYearning for the impossible : the surprising truths of mathematicsElements of number theory
Alternative Names
John Stillwell Australian mathematician

John Stillwell Australisch wiskundige

John Stillwell australischer Mathematiker

John Stillwell matemàtic australià

John Stillwell matemático australiano

John Stillwell matematikan australian

John Stillwell mathématicien australien

Stillwell, J.

Stillwell, J.C., 1942-

Stillwell, J. (John)

Stillwell, J.‏ (John), 1942-

Stillwell, John

Stillwell, John, 1942-

Stillwell, John C.

Stillwell, John C. 1942-

Stillwell, John C. H.

Stillwell, John C. (John Colin)

Stillwell, John Colin 1942-

ג'ון סטילוול מתמטיקאי אוסטרלי

スティルウェル, J

スティルウェル, ジョン

约翰·史迪威

Languages
English (334)

German (9)

Italian (1)

Chinese (1)